Solar Cells Thin Film Technologies Part 6 pot

Crystalline Silicon Thin Film Solar Cells 139 thermal annealing step at 900°C follows The silicon layers are passivated by a hydrogen plasma treatment Finally rather demanding structuring and contacting processes follow In production, modules 1x1.4 m² in size reached about 7% efficiency In the lab 10.4% efficiency were achieved on 92 cm² minimodules (Keevers et al., 2007) The production was stopped, probably because of the high cost PECVD deposition, which was used because the method was the only one available for silicon deposition in the m² range In the lab, high rate electron beam evaporation was tested as an alternative which delivered minimodules with the efficiency of 6.7%, similar to that of the industrially produced modules (Egan et al., 2009; Sontheimer et al., 2009) The grain size originating in the furnace anneal is dictated by the interplay of crystal nucleation within the amorphous matrix and growth of the nuclei (see Sect 5) One can influence both processes by the temperature of the annealing step Practically, however, there is not much choice At lower temperature the annealing time required for complete crystallization would reach unrealistic high values so that this is not possible in production Higher temperatures are not endured by the glass substrate for the time span needed for crystallization Even at 600°C 18 h are required for crystallization and high temperature resistant borosilicate glass has to be used instead of a much cheaper soda lime glass As an alternative for the furnace crystallization pulsed excimer laser crystallization via the melt is a process industrially used in flat panel display production For this application, however, rather thin films ( 10 µm 3.1 Basic considerations As mentioned in the last paragraph, grains larger than about µm cannot be prepared by direct deposition of crystalline silicon, nor by solid phase crystallization of a-Si nor via melting a-Si by short laser pulses Large grains can be produced from the melt only if the melt is cooled below the equilibrium melting point slowly so that the melt stays long enough in a region of low nucleation rate and there is time enough for the few nucleating crystallites to grow to large size Low cooling rate means low heat flow into the substrate following from a low temperature gradient in the substrate This can be achieved if the melting time of the silicon layer is larger than in excimer laser crystallization, i.e much larger than 100 ns To reach longer melting times the energy for melting has to be delivered on a longer time scale For energy delivery scanned electron beams or scanned laser beams have been used However, the longer melting time has the consequence, that dopand profiles, introduced into the virgin a-Si for emitter, absorber, and back surface field, get intermixed due to diffusion Typical diffusion constants in liquid silicon are in the 10-4 to 10-3 cm²/s range (Kodera, 1963) so that dopands will intermix over a distance of µm within 10 to 100 µs Nevertheless a one-step crystallization procedure for a solar cell layer system has been done by electron beam melting, discussed in Sect 3.2 Alternatively a two-step procedure has been used In a first step a thin seed layer is crystallized to large grains from a-Si by laser irradiation In a second step the seed is thickened epitaxially Seed and epitaxial layer can be differently doped so that the seed can act as the emitter and the epitaxial layer as the absorber of the solar cell Alternatively, the seed may act as a highly doped back surface field layer with the epitaxial layer acting as a moderately doped absorber The emitter is generated on top in a third preparation step 140 Solar Cells – Thin-Film Technologies An important issue in any of the mentioned preparation steps is the choice of the substrate This choice depends on the thermal load the substrate experiences during the silicon crystallization process Plastic substrates are not useful for any of the processes described in Sect since the substrate temperature well exceeds 200°C One usually divides the crystallization methods into low temperature processes for which glass can be used as a substrate and high temperature processes for which glass is not sufficient Instead, ceramics (e.g alumina) or graphite has been used These substrate materials, however, are much more expensive than glass so that the economic consequences for the high temperature routes are not so pleasant Typically, in high as in low temperature processes some barrier layer is used to prevent the diffusion of foreign atoms from the substrate material into the silicon layer during the processing steps The barrier layer has to fulfil different requirements except of its main purpose First of all it has to withstand liquid silicon, i.e it should not decompose or react with the silicon melt Moreover, it should not release gases which would blow off the silicon layer Then it should be well wetted by liquid silicon Otherwise the silicon film during melting could dewet to form droplets This latter requirement is the reason that SiO2 is not useful as a barrier layer Silicon nitride or silicon carbide are better suited However, if deposited by PECVD the layers contain too much hydrogen which is released during silicon melting so that the silicon films are destroyed According to our experience sputtered silicon nitride is well suited if prepared correctly 3.2 Single step layer preparation - electron beam crystallization As mentioned in Sect 3.1 silicon solar cell absorbers in substrate configuration have been prepared by electron beam crystallization in a one step process (Gromball et al., 2004; Amkreuz et al., 2009) On a glass substrate with a barrier layer (e.g SiC) to 15 µm of pdoped (1017 cm-3 B) nanocrystalline silicon was deposited by high rate (up to 300 nm/min) PECVD from trichlorosilane This layer was crystallized by scanning a line shaped electron beam (15 cm x mm) At a scanning rate of cm/s a beam energy density of 500mJ/cm² has been used so that any position is treated for about 0.1 s The resulting grain size is in the mm range To get a solar cell a 30 nm thick n-doped a-Si heteroemitter was deposited onto the crystalline absorber by PECVD The maximum solar cell parameters achieved so far were jsc = 12.4 mA/cm², Voc = 487 mV, and an efficiency of 3.5% (Amkreuz et al., 2009) Obviously the absorber doping is too high and a back surface field is missing Work is ongoing to improve these cells 3.3 Two-step process - seed preparation In the two-step preparation method first a thin seed layer with the desired crystal structure is prepared which can be used as a back surface field layer or as emitter in the final solar cell The absorber is then prepared by epitaxial thickening of the seed In case of a cell in superstrate configuration (illumination through the glass), the seed layer should be rather thin This is to reduce light absorption in the seed which is highly doped (as emitter or as back surface field layer) and shows only low photovoltaic activity Two seed preparation methods have been investigated: aluminium induced crystallization (Fuhs et al., 2004) as well as laser crystallization 3.3.1 Aluminum induced crystallization for seed preparation Aluminum induced crystallization (AIC) works as follows: On to the substrate an aluminum layer is deposited by sputtering or evaporation On top follows an amorphous silicon layer Crystalline Silicon Thin Film Solar Cells 141 When the Al/a-Si layer system is heated (350°C…550°C below the eutectic temperature of the Al-Si system at 577°C) a layer exchange process takes place combined with silicon crystallization, which is completed, at 500°C, in about 30 (Pihan et al., 2007) Finally, a crystalline silicon layer rests on the glass and is covered by an aluminium layer, which may contain silicon islands The silicon layer is highly p-doped typically by 1019 cm-3 Al (Antesberger et al., 2007) It has been reported that the details of the process and the properties of the final silicon layer depend on the thickness of an aluminum oxide layer which was present between Al and a-Si before the tempering step Typical resulting silicon grain sizes are in the range of 10 µm The preferred grain orientation is (100) but other orientations occur as well (Schneider et al., 2006a) Typical layer thicknesses are 300 nm for Al and 375 nm for Si (Fuhs et al., 2004), which is a bit high for seed layers However, even silicon films thinner than 100 nm have been crystallized by AIC (Antesberger, 2007) Some work has been done to understand the thermodynamics and the kinetics of the process (Wang et al., 2008; Sarikov et al., 2006; Schneider et al., 2006b) It seems that silicon diffuses through the thin alumina layer into the aluminum where it preferably further diffuses towards the glass along the aluminum grain boundaries When aluminum gets supersaturated by silicon, nucleation of silicon crystallites starts preferably at the interface to the glass substrate The driving force for the process is the free energy difference between metastable amorphous and absolutely stable crystalline silicon Finally, the a-Si completely has diffused through the aluminum which then rests on top Before the crystalline silicon layer can be used as a seed, the aluminum layer has to be removed, e.g by wet chemical etching using HCl Challenging is the removal of the silicon islands included in the aluminum layer and of the aluminum oxide film The removal of both is crucial for good epitaxy (Rau et al., 2004) The inverse process with the starting sequence glass/a-Si/Al and the final sequence glass/Al/cSi works as well (Gall et al., 2006) It has some advantages for cells in substrate configuration, e.g that a Al back contact is formed automatically However, the Al/Si contact has the consequence that any further processing steps, e.g epitaxy, cannot be performed above the eutectic temperature of the Al-Si system of 577°C For this reason the inverse process was abandoned There has been done a lot of work on silicon crystallization by other metals, e.g Au, Ni, but these methods did not find application in solar cell preparation 3.3.2 Laser crystallization for seed preparation To get large silicon crystals by laser crystallization the beam of a cw laser is scanned so that the irradiation time at each position is in the ms range, much larger than during pulse laser irradiation mentioned in Sect Under these conditions the temperature gradient and therefore the heat flow in the substrate is low so that the melt undercools only slowly, nucleation rates are low, and nucleated crystals have time enough to grow to large sizes (see Sect 5) First results on this method date back to the late 1970ies (Gat et al., 1978; Colinge et al., 1982) At these times laser crystallization was performed for applications in microelectronics Therefore amorphous silicon on wafers covered by oxide was used as starting material The only available well suited lasers were argon ion lasers emitting green light at 514 nm wavelength with a total power of up to 15 W Typically a circular Gaussian beam with diameter in the 40 µm range was scanned across the sample At a scanning rate of 12.5 cm/s already in 1978 grains 2x25 µm in size were produced (Gat et al., 1978) Due to the high thermal conductivity of the wafer substrate a rather high power density is needed for melting and crystallization in this case Only later glass was discovered as a useful substrate 142 Solar Cells – Thin-Film Technologies for thin film transistor applications (Michaud et al., 2006) as well as for solar cells (Andrä et al., 1998; Andrä et al 2000) On glass with low thermal conductivity power densities of about 20 kW/cm² are needed at scanning speeds of several cm/s Due to the limited laser power the spot diameter was limited to about 100 µm Fig Optical micrograph of a silicon layer crystallized by scanning the circular beam of an argon ion laser Left: single scan; right: overlapping scans Fig (left) shows an optical micrograph of a single trace produced by scanning a circular Ar ion laser beam At the rim very fine crystals were produced There the laser power just was able to generate a temperature a bit above the melting point of a-Si, which is well below the melting point of crystalline silicon (see Sect 5.1) In the rim region a strongly undercooled melt is generated which immediately (that is must faster than the irradiation time) crystallizes to fine grained (about 100 nm) silicon Towards the center of the trace the power density increases so that the temperature gets higher, the undercooling gets lower, and a bit larger grains solidify In the central part the laser power is high enough to produce a silicon melt above the equilibrium melting point of crystalline silicon (1412°C) There solidification occurs only when the laser beam already has passed The slowly undercooling liquid silicon is in contact with the small crystallites of the rim region which crystallized earlier From these, lateral epitaxial growth takes place The crystallization direction coincides with the temperature profile following the scanned laser beam Those of the many nuclei are successful in epitaxy for which the fastest crystallographic growth direction coincides with the temperature gradient Therefore, a selection mechanism is active and only few of the potential nuclei grow As a consequence large grains form several 10 µm wide and over 100 µm long To get not just one crystalline trace but a completely crystallized area, one just has to scan the laser beam in overlapping rows (Fig 1, right) In the second row the laser beam remelts part of the previous row with the consequence that now the melt is in contact with the large grains produced in the previous row Therefore large crystals are already present for lateral epitaxy to occur In this way large areas covered by large grains can be produced Defect population in films generated in this way has been investigated (Christiansen et al., 2000) The dislocation density was rather low Grain boundaries are mostly Σ3 and Σ9 twin boundaries which are expected to be not active electrically The grain orientation is at random with no preferential texture Later on, for crystallization the argon ion laser was replaced by a solid state cw Nd:YAG laser, emitting green light of 532 nm wavelength after frequency doubling Similar results were obtained with this laser type (Andrä et al., 2005a) Both, argon ion as well as Nd:YAG lasers, 143 Crystalline Silicon Thin Film Solar Cells have rather limited power so that it is impossible to crystallize seed layers for large area solar cells in an industrial environment For example, a m² module would require many hours laser treatment Therefore, when looking for high power lasers we ended up with diode lasers, emitting in the near infrared However, the absorption coefficient of a-Si for 806 nm radiation, the shortest wavelength available for high power diode lasers, at room temperature is only about 0.3 µm-1, as compared to 25 µm-1 for green light Fig shows the absorption of 806 nm radiation in amorphous silicon (electron beam deposited, hydrogen free) as calculated from optical properties (n and k) measured from room temperature up to 600°C and extrapolated up to 1000°C The maxima and minima are due to interference effects in the silicon layer Obviously there exists a problem for thin films, particularly at room temperature In thin films, only a small amount of the incoming radiation is absorbed at room temperature Therefore, to heat the silicon film, a rather high power density is needed When heating started successfully then the absorption increases and a run-off sets in which is only limited after melting, when the reflectivity jumps up So the process has some inherent instability, which can be handled only when one preheats the substrate to about 600°C so that laser heating starts at a higher absorption already The substrate heating has another positive effect, namely to reduce the cracking tendency of the glass substrate, for which we use a borosilicate glass (Schott boro 33) with a thermal expansion coefficient very near to that of silicon Work using diode lasers for crystallization started 2006 (Andrä et al., 2006) For our seed layer crystallization we use LIMO line focus lasers (806 nm wavelength, 13 mm x 0.1 mm focus and 30 mm x 0.1 mm focus) with maximum power density of up to 25 kW/cm² (Andrä et al., 2006), allowing for scanning speeds up to several cm/s Fig shows an EBSD map of a crystallized region demonstrating large grains in the 100 µm range in 450 nm thick films With the diode laser we can go down to 100 nm thin films In these the grains size is in the 30 µm range A further problem with thin films is dewetting This means that holes form when the silicon film is liquid It even happens that the holes grow to large sizes and only a part of the substrate is covered by silicon Dewetting can be reduced if the wetting angle of liquid silicon on the substrate is low This can be influenced by the barrier layer on the glass substrate ,7 ,6 Absorption ,5 ,4 ,3 ,2 ,1 ,0 100 200 300 400 00 600 700 800 900 1000 Film Thickness [nm] Fig Absorption of 806 nm diode laser radiation in an amorphous silicon thin film on glass as depending on film thickness Film temperature 20°C (blue), 600°C (red), and 1000°C (black) 144 300 µm Solar Cells – Thin-Film Technologies 100 µm Fig EBSD map (inverse pole figure) of diode laser crystallized seed layers 450 nm (left) and 110 nm (middle) thick Color code for grain orientation is shown on the right Concerning the throughput, laser companies are just developing line focus diode lasers with long lines (Lichtenstein 2010) which would allow crystallization of a m² module within minutes If seed layers thinner than 100 nm are to be crystallized diode lasers cannot be used due to too low absorption even when preheated We tested a pulsed green laser (JenLas ASAMA) emitting 515 nm wavelength radiation (Andrä et al., 2010) This laser has a line focus up to 100 mm long and to 10 µm wide and it delivers 600 ns pulses at a repetition rate of up to 80 kHz At a fluence of about 1.2 J/cm² the sample was shifted 1.5 µm between subsequent pulses In this way 60 nm thin seed layers were crystallized without any preheating with resulting grains several µm wide and several 10 µm long (Fig 4) Obviously, the melt generated during each laser pulse solidifies by lateral epitaxy so the grains generated by the previous pulse grow stepwise Finally long grains form, which continue over many pulses Since the width of the melt is µm in our case and the melt exists for a time interval in the several µs range, the solidification speed is in the m/s range This value is near the maximum following from solidification kinetics (see Sect 5) Fig EBSD map (inverse pole figure) of pulse laser crystallized seed layers 60 nm thick Crystalline Silicon Thin Film Solar Cells 145 3.4 Two step process - epitaxial thickening In the two step preparation method on top of the multicrystalline seed layer the absorber of the solar cell is prepared by epitaxial growth Several methods have been used which can be classified into direct epitaxial deposition and deposition as amorphous silicon followed by epitaxial crystallization, either in the solid state by furnace or by laser annealing or via laser melting Particularly in the cases without melting the cleanliness of the interface between crystalline seed and amorphous silicon to be epitaxially crystallized is an issue Any contaminants present, even small amounts of a monolayer, will jeopardize epitaxial crystallization or at least increase the amount of extended defects in the epitaxial layer appreciably First of all, any silicon oxide has to be removed from the seed surface This can be achieved by HF A 2% to % solution in water is most useful Success can be observed by the naked eye When HF has removed the oxide the silicon surface gets hydrogenated which makes the surface hydrophobic and the etching solution dewets, i.e forms droplets Then the HF solution can be blown off by nitrogen The hydrogenated surface state remains stable in ambient air at room temperature for about h so that there is time enough to introduce the sample into a deposition chamber for a-Si deposition However, other possible contaminants are not so easily removed It turned out as useful to start with an RCA cleaning step before HF treatment The RCA step removes e.g organic contaminants 3.4.1 Direct epitaxial deposition The simplest epitaxial thickening procedure is direct epitaxial deposition of silicon on top of the seed layer Several processes have been investigated in the past, high temperature CVD and, at intermediate temperature, electron beam evaporation, ECRCVD, and hot wire CVD The high temperature route has been reviewed recently (Beaucarne et al., 2004) The highest efficiency reached so far with this method is 8% (Gordon et al., 2007) On an alumina substrate seed layers were prepared by aluminium induced crystallization Epitaxial thickening for the p-doped absorber with rates up to 1.4 µm/min was done by thermal CVD at 1130°C from trichlorosilane The final emitter was prepared by phosphorus diffusion, or an a-Si heteroemitter was deposited by PECVD Corresponding to the seed layer the grain size in the absorber is several 10 µm It is expected that the efficiency is not so much limited by the grain size but by intragrain defects, which have been thoroughly investigated (van Gestel et al., 2009) Even higher efficiencies of 11.1% were reached on seed layers crystallized by lamp heater zone melting on graphite and high temperature epitaxy for absorber growth (Kunz et al., 2008) The high temperature process has the advantage that it works on any grain orientation of the seed However, high temperature resistant substrates such as alumina, silica, glass ceramics, or graphite are needed, which are not very feasible for large scale production At intermediate temperature both, electron beam evaporation, partly modified by ion assisted deposition, or ECR-CVD (electron cyclotron resonance CVD) has been tested for epitaxy on AIC seed layers ECR-CVD was successfully applied at 585°C substrate temperature (Rau et al., 2004) However, epitaxy worked well only on (100)-oriented grains, which is the most common orientation following from AIC, but not the only one At 670°C epitaxy by hot wire CVD worked on any grain orientation with a rate of 100 nm/min Ion assisted deposition, that is electron beam evaporation plus some ionization of the silicon atoms, was tested for epitaxy as well For the deposition a temperature ramp was carefully optimized with maximum temperature below 700°C The deposition rate was 300 nm/min The highest achieved open circuit voltage of solar cells was 453 mV (Straub et al., 2005) Direct epitaxy during electron 146 Solar Cells – Thin-Film Technologies beam evaporation at 550°C substrate temperature has successfully been demonstrated (Dogan et al., 2008) Solar cells prepared with this process reached 346 mV open circuit voltage and 2.3% efficiency, which is a bit low as compared to the values achieved by other methods 3.4.2 Solid phase epitaxy in furnace Technically the most simple way to achieve epitaxial growth is to deposit first an amorphous layer on top of the cleaned seed layer, and then to epitaxially crystallize the layer by furnace annealing in the solid state The layer to be crystallized can already contain the desired doping profile which remains during the annealing step The main critical point with this simple procedure is that not only an epitaxial crystallization front moves into a-Si, but also spontaneous nucleation will occur within a-Si followed by growth of crystallites So there exists a competing process to the desired epitaxy The question arises, which of the two succeeds The speed of the epitaxial front of course depends on temperature (described by Jackson-Chalmers equation, see Sect 5.1) and so does nucleation, described by classical nucleation theory (Sect 5.2), and growth of nuclei, the latter phenomena described together by Avrami-Mehl equation (Sect 5.4) An important point, which makes SPE possible, is that, if no nuclei pre-exist in the amorphous matrix, nucleation does not start immediately Instead it needs some time, called time lag of nucleation, until a stationary population of nuclei evolves (Sect 5.3) Only after that time lag the stationary nucleation rate applies at fixed temperature, described by classical nucleation theory, and crystal nuclei appear So any successful epitaxy relies on the time lag of nucleation The thickness of an epitaxially crystallized layer is just given by the time lag of nucleation times the speed of the epitaxial crystallization front After the time lag, in the virgin amorphous silicon crystalline nuclei of random orientation appear resulting in fine grained material, such as is generated by direct furnace crystallization (see Sect 2) without seed For successful epitaxy one has to make sure that within the amorphous phase there are no nuclei present which could form during deposition already In the last few years we developed the technique of SPE on diode laser crystallized seed layers on borosilicate glass substrates (Andrä et al., 2008a; Schneider et al., 2010) The virgin a-Si layers including a doping profile were deposited at high rate (typically 300 nm/min) by electron beam evaporation at a substrate temperature in the 300°C range At that temperature no nuclei form within a-Si The layer system was then annealed in a furnace under ambient air To control the progress of crystallization, an in situ measurement technique was installed For this purpose, the beam of a low power test laser was sent through the sample The transmitted intensity was monitored by a photocell Since a-Si has a different optical absorption from c-Si, the progress of crystallization can be monitored easily In particular, the crystallization process is complete when the transmission does not change any more Fig shows a transmission electron micrograph of a cross section of an epitaxially thickened silicon film Fig Transmission electron microscopic cross section image of a film epitaxially thickened by furnace annealing Crystalline Silicon Thin Film Solar Cells 147 In summary we could epitaxially crystallize up to 1.6 µm of a-Si at a temperature of 630°C within h The epitaxial quality as determined by EBIC was best in (100) oriented grains and worst in (111) grains Moreover, the epitaxial crystallization speed depends on orientation and on the doping level Higher doped layers crystallize faster Solar cells prepared on these layers reached an efficiency of 4.9% after hydrogen passivation (Schneider et al., 2010) By TEM cross section investigations it was shown that the seed layers contain only very few extended defects such as dislocations, whereas the epitaxial layer contains much more It seems that the cleaning procedure of the seed surface prior to a-Si deposition is crucial for good epitaxial quality At least the dislocation density in the epitaxial layer could be reduced by an additional RCA cleaning step before removal of oxide by HF However, this did not reflect in the achieved solar cell efficiencies 3.4.3 Layered laser crystallization The epitaxy method of layered laser crystallization has been developed in our group years ago (Andrä et al 2005b, Andrä et al., 2008a) The principle is simple During deposition of aSi on top of the seed layer excimer laser pulses are applied repeatedly, which melt the newly deposited a-Si and a bit of the crystalline silicon beneath so that after each pulse epitaxial solidification occurs Again, the layer thickness to be crystallized by one laser shot is limited by a competing nucleation process in the undercooling melt after the laser pulse According to our experience about 200 nm of a-Si can be epitaxially crystallized by one laser pulse The typical laser fluence needed is 550 mJ/cm² However, when during the whole thickening process the thickness of the crystalline layer beneath the newly deposited a-Si increases from the initial seed layer (say 200 nm) to the final absorber thickness (say µm) the laser parameters or the thickness of the newly deposited a-Si have to be adjusted so that the laser pulse just melts the a-Si and bit of c-Si beneath This adjustment is necessary because the thermal properties of glass, c-Si, and a-Si differ so that the temperature profiles change during the process if the laser energy would be kept constant In the layered laser crystallization process epitaxy works independently of the grain orientation, which is an advantage since crystal orientation in the seed is at random For the process, the laser pulse has to be fed through a window in the deposition chamber onto the growing layer In this way the pulses can be applied without stopping deposition For a-Si deposition we use electron beam evaporation which has first the advantage of high deposition rate, at least an order of magnitude higher than for PECVD, and secondly the advantage that deposition is directed so that no deposition occurs at the laser window Doping is achieved by codeposition of boron or phosphorus In our device we can deposit and laser irradiate substrates of up to 10x10 cm² The single laser spot has a size of 6x6 mm² with top hat profile To cover the whole substrate area the laser spot is scanned over the substrate by a scanning mirror placed outside the deposition chamber In order to avoid cracks in the glass substrate heating to about 600°C helps Upscaling the system to m² surely is a challenge but not outside the technical possibilities If properly optimized, about 10 laser pulses are needed at each position during absorber deposition to prepare a µm thick epitaxial film This makes sense only if the laser is fed into the deposition chamber and is applied without braking deposition, as we it in our lab scale equipment In the epitaxial layer prepared by layered laser crystallization the number of extended defects like dislocations is much lower as compared to solid state epitaxy This is because the mobility of crystallizing atoms is much higher in the melt than in a-Si so that correct placement is easier The highest efficiencies achieved in solar cells prepared using the 148 Solar Cells – Thin-Film Technologies method were 4.8% at an open circuit voltage of 517 mV (Andrä et al., 2005b; Andrä et al., 2007) These values were measured on cells without any light trapping 3.4.4 Liquid or solid phase epitaxy by diode laser irradiation The layered laser crystallization method described in the last section has the drawback that up-scaling into the industrial scale is not so easy This is due to the fact, that the laser beam has to be fed into the deposition chamber and several pulses have to be applied at each position That was the motivation for us to look for a method in which the complete absorber thickness is deposited in the amorphous state on top of the seed and to apply a single laser treatment to epitaxially crystallize the whole system in one run after deposition outside the deposition chamber The most obvious way to achieve epitaxy is via the liquid phase similar to layered laser crystallization The main difference is that the whole amorphous absorber precursor layer is melted in one step down to the seed, so that epitaxial solidification is to occur after irradiation It is a challenge to melt about µm of a-Si without completely melt the about 200 nm thin c-Si seed beneath which would hamper any epitaxy To crystallize a layer system more than µm thick, a short pulse laser is useless To get the required energy into the system the pulse fluence would have to be so large that ablation would occur at the surface Moreover, the cooling rate of the melt after a short laser pulse would be so high, that nucleation is expected to occur in a surface near region before the epitaxial solidification front reaches the surface Therefore we decided to use a scanned cw diode laser for this purpose with irradiation times in the ms range In this case the cooling rate is low enough so that the melt stays long enough in a slightly undercooled state with low nucleation rate until the epitaxial solidification front reaches the surface We succeeded in epitaxially crystallizing 500 nm in one run However, forming of cracks is an issue Moreover, due to the strong diffusion in the melt which intermixes any pre-existing doping profile, absorber and emitter cannot be crystallized in one step An alternative is solid phase epitaxy in which the amorphous layer is heated by the laser to a temperature of about 1100°C, below the melting point of a-Si At such high temperature the solid phase epitaxial speed was determined to several 100 nm/s high so that epitaxy of µm should be complete within several seconds Post-crystallization treatment 4.1 Emitter preparation The emitter of the final solar cell can be prepared in different ways One is to include emitter doping into the deposition sequence of the layer system so that no additional emitter preparation step is needed This way has been chosen in the CSG process and in layered laser crystallization It cannot be applied in case of liquid phase epitaxy of the whole layer stack (Sect 3.4.4) since during melting for several ms, diffusion in the liquid state would intermix any dopand profile introduced during deposition In this case, phosphorus doping of a boron doped absorber as in conventional wafer cells can be performed The only difference is that the doping profile has to be much shallower Another variant is to use amorphous heteroemitters IMEC has found that this is the best emitter for their thin film solar cells prepared by the high temperature route (Gordon et al., 2007) 154 Solar Cells – Thin-Film Technologies 5.4 Complete kinetics of transformation Stationary nucleation together with the growth of supercritical nuclei according to the Jackson-Chalmers equation leads to a continuous increase of the amount of the new phase on account of the parent phase When one takes account that during the progress of phase transformation more and more parent phase is consumed and less volume is available for actual transformation, one ends up with the Avrami-Mehl equation (Avrami, 1940) for the volumetric amount of the new phase     et 4 /tc (9) with the characteristic time tc   Jv (10) J is the stationary nucleation rate of Eq and v is the speed of propagation of a phase front according to Jackson-Chalmers Eq In deriving Eq the time lag of nucleation τ has been neglected To include this effect, one simply replaces t by (t-τ) in Eq for t>τ The resulting average grain size when the parent phase has been consumed completely is given by D  1.037 v J (11) So the grains are the larger the higher the Jackson-Chalmers speed and the lower the nucleation rate is, which sounds reasonable To get large grains from an undercooled melt one should keep the temperature in a range of not too high undercooling, where nucleation rate is low and growth rate is high (Figs and 8) Fig 12 shows the expected final grain size in solid phase crystallization of amorphous silicon It shows that in the CSG process at about 600°C (see Sect 3.) grains of several µm are to be expected, which is in accordance with experiments By increasing the crystallization temperature one cannot change the grain size appreciably Lowering the temperature would lead to a rather high time needed for crystallization due to higher time lag of nucleation (Fig 11), lower nucleation rate (Fig 9), and lower growth rate (Fig 7) D/µm 100 Tma 10 600 800 1000 1200 1400 T/K Fig 12 Average grain size after solid phase crystallization of amorphous silicon as depending on temperature Crystalline Silicon Thin Film Solar Cells 155 Conclusion Multi- and polycrystalline silicon thin film solar cells receive growing interest worldwide Presently, the maximum efficiency reached by these types of cells is 10.4% Different cell concepts and preparation methods are under investigation and no clear favourite way is identified up to now The concepts differ in the resulting grain structure, i.e size and quality, but also in the preparation technologies used and the processing time needed Today it is not clear which of the methods will succeed in industrial production In all the methods, pin holes in the films are an issue since they lead to shunting of the final cells Another issue is dopand deployment, particularly along grain boundaries This also may lead to shunting, which today limits the open circuit voltage to slightly above 500 mV A further point is that TCO cannot easily be used as a front contact in superstrate cells since it hardly withstands the temperatures needed for crystallization Usually a highly doped silicon layer is used instead, which, however, has somewhat low transparency Very important for thin film crystalline solar cell is a perfect light management so that about µm of silicon is enough to absorb the solar spectrum This can be achieved either by structured substrates or by texturing the surface In the first case, the irregular substrate surface should not influence the crystallization behaviour In the second case, the rough surface should not increase surface recombination Generally, passivation of defects and of the surface is a crucial preparation step Concerning the theoretical description of the processes involved in crystallization, the basic equations are well understood However, there are some issues with the material parameters involved, which, particularly for amorphous silicon, strongly depend on deposition conditions and therefore need to be determined individually But even if numerical predictions may not completely coincide with experiments due to inadequate numerical values of the materials parameters, general trends can reliably be predicted All the mentioned issues need further investigation Careful study of these topics is expected to lead to full exploitation the potential of the material Multicrystalline thin film cells with a ratio of grain size over film thickness similar to multicrystalline wafer cells should deliver, if prepared correctly, comparable efficiencies Therefore we expect the polyand multicrystalline silicon thin film solar cells to gain increasing significance and may replace microcrystalline silicon cells Multicrystalline silicon also can act as one partner in tandem cells which would further increase the efficiency Acknowledgment This work partly was funded by the European Commission under contract 213303 (HIGHEF), and by the German state of Thuringia via Thüringer Aufbaubank under contract 2008 FE 9160 (SolLUX) We would like to thank J Lábár and G Sáfrán (MFA Budapest) for TEM investigations References Amkreutz, M.; Müller, J.; Schmidt, M.; Haschke, J.; Hänel, T & Schulze, T.F (2009) Optical and electrical properties of electron beam crystallized thin film silicon 156 Solar Cells – Thin-Film Technologies solar cells on glass substrates Proc 24th Europ Photovoltaic Solar Energy Conf., pp 2506-2509 Andrä, G.; Bergmann, J.; Falk, F.; Ose, E & Stafast, H (1998) Laser Induced Crystallization of Amorphous Silicon Films on Glass for Thin Film Solar Cells Physica status solidi (a), Vol 166, pp 629-634 Andrä, G.; Bergmann, J.; Falk, F & Ose, E (2000) Preparation of single crystalline regions in amorphous silicon layers on glass by Ar+ laser irradiation Applied Surface Science, Vol 154-155, pp 123-129 Andrä, G.; Bergmann, J & Falk, F (2005a) Laser crystallized multicrystalline silicon thin films on glass Thin Solid Films, Vol 487, pp 77-80 Andrä, G.; Bergmann, J.; Bochmann, A.; Falk, F.; Dauwe, S & Kieliba, T (2005b) Characterization and simulation of multicrystalline LLC-Si thin film solar cells Proc 20th Europ Photovoltaic Solar Energy Conf., pp 1171-1174 Andrä, G.; Bochmann, A.; Falk, F.; Gawlik, A.; Ose, E & Plentz J (2006) Diode laser crystallized multicrystalline silicon thin film solar cells on glass Proc 21st Europ Photovoltaic Solar Energy Conf., pp 972-975 Andrä, G.; Plentz, J.; Gawlik, A.; Ose, E.; Falk, F & Lauer, K (2007) Advances in multicrystalline LLC-Si thin film solar cells Proc 22nd Europ Photovoltaic Solar Energy Conf., pp 1967-1970 Andrä, G.; Gimpel, T.; Gawlik, A.; Ose, E.; Bochmann, A.; Christiansen, S.; Sáfrán, G.; Lábár, J.L & Falk, F (2008a) Epitaxial Growth of Silicon Thin Films for Solar Cells Proc 23rd Europ Photovoltaic Solar Energy Conf 2008, pp 2194-2198 Andrä, G.; Lehmann, C.; Plentz, J.; Gawlik, A.; Ose, E & Falk, F (2008b) Varying the Layer Structure in Multicrystalline LLC-Silicon Thin-Film Solar Cells Proc 33rd IEEE Photovoltaic Specialists Conf., pp 457-462 Andrä, G.; Bergmann, J.; Gawlik, A.; Höger, I.; Schmidt, T.; Falk, F.; Burghardt, B & Eberhardt, G (2010) Laser Induced Crystallization Processes for Multicrystalline Silicon Thin Film Solar Cells Proc 25th Europ Photovoltaic Solar Energy Conf 2010, pp 3538-3542 Antesberger, T.; Jaeger, C.; Scholz, M & Stutzmann, M (2007) Structural and electronic properties of ultrathin polycrystalline Si layers on glass prepared by aluminuminduced layer exchange Applied Physics Lett., Vol 91, pp 201909 Avrami, M (1940), Kinetics of Phase Change II Transformation-Time Relations for Random Distribution of Nuclei, J Chemical Physics, Vol 8, pp 212-224 Beaucarne, G.; Bourdais, S ; Slaoui, A & Poortmans, J (2004) Thin-film polycrystalline Si solar cells on foreign substrates : film formation at intermediate temperatures (7001300°C) Applied Physics A, Vol 79, pp 469-480 Beaucarne, G.; Gordon, I.; van Gestel, D.; Carnel, L & Poortmans, J (2006) Thin-film polycrystalline silicon solar cells: An emerging photovoltaic technology Proc 21st European Photovoltaic Solar Energy Conference, pp 721-725 Beaucarne, G (2007) Silicon thin-film solar cells Advances in OptoElectronics, Vol 2007, Article ID 36970 Crystalline Silicon Thin Film Solar Cells 157 Brazil, I & Green, M.A (2010) Investigating polysilicon thin film structural changes during rapid thermal annealing of a thin film crystalline silicon on glass solar cell J Materials Sci.: Materials in Electronics, Vol 21, pp 994-999 Brendel, R (2001) Review of layer transfer process for crystalline thin-film silicon solar cells Japanese J Applied Physics, Vol 40, pp 4431-4439 Brendel, R.; Feldrapp, K.; Horbelt, R & Auer, R (2003) 15.4%-efficient and 25 µm-thin crystalline Si solar cell from layer transfer using porous silicon Physica status solidi (a), Vol 197, pp 497-501 Christiansen, S.; Nerding, M.; Eder, C.; Andrae, G.; Falk, F.; Bergmann, J.; Ose, E & Strunk H.P (2000) Defect population and electrical properties of Ar+-laser crystallized polycrystalline silicon thin films Materials Res Soc Symp Proc., Vol 621, art Q7.5.1 Colinge, J.P.; Demoulin, E.; Bensahel, D & Auvert, G (1982) Use of selective annealing for growing very large grain silicon on insulator films Applied Physics Lett., Vol 41, pp 346-347 Dogan, P.; Rudigier, E.; Fenske, F.; Lee, K.Y.; Gorka, B.; Rau, B.; Conrad, E & Gall, S (2008) Structural and electrical properties of epitaxial Si layers prepared by e-beam evaporation Thin Solid Films, Vol 516, pp 6989-6993 Donovan, E.P.; Spaepen, F.; Turnbull, D.; Poate, J.M & Jacobson, D.C (1983) Heat of crystallization and melting point of amorphous silicon Applied Physics Lett., Vol 42, pp 698-700 Egan, R.; Keevers, M.; Schubert, U.; Young, T.; Evans, R.; Partlin, S.; Wolf, M.; Schneider, J.; Hogg, D.; Eggleston, B.; Green, M.; Falk, F.; Gawlik, A.; Andrä, G.; Werner, M.; Hagendorf, C.; Dogan, P.; Sontheimer, T & Gall, S (2009) CSG minimodules using electron-beam evaporated silicon Proc 24th Europ Photovoltaic Solar Energy Conf 2009, pp 2279-2285 Falk, F & Andrä, G (2006), Laser crystallization – a way to produce crystalline silicon films on glass or polymer substrates J Crystal Growth, Vol 287, pp 397-401 Fogarassy, E; de Unamuno, S.; Legagneux, P.; Plais, F.; Pribat, D.; Godard, B & Stehle, M (1999) Surface melt dynamics and super lateral growth regime in long pulse duration excimer laser crystallization of amorphous Si films Thin Solid Films, Vol 337 pp 143-147 Fuhs, W.; Gall, S.; Rau, B.; Schmidt, M & Schneider, J (2004) A novel route to a polycrystalline silicon thin-film solar cell Solar Energy, Vol 77, pp 961-968 Gall, S.; Schneider, J.; Klein, J.; Hübener, K.; Muske, M.; Rau, B.; Conrad, E.; Sieber, J.; Petter, K.; Lips, K.; Stöger-Pollach, M.; Schattschneider, P & Fuhs, W (2006) Largegrained polycrystalline silicon on glass for thin-film solar cells Thin Solid Films, Vol 511, pp 7-14 Gat, A.; Gerzberg, L.; Gibbons, J.F.; Magee, T.J.; Peng, J & Hong, J.D (1978) cw laser anneal of polycrystalline silicon: Crystalline structure, electrical properties Applied Physics Lett., Vol 33, pp 775-778 Gordon, I.; Carnel, L.; Van Gestel, D.; Beaucarne, G & Poortmans, J (2007) 8% efficient thinfilm polycrystalline-silicon solar cells based on aluminum-induced crystallization and thermal CVD Progress in Photovoltaics, Vol 15, pp 575-586 158 Solar Cells – Thin-Film Technologies Green, M.A.; Basore, P.A.; Chang, N.; Clugsto, D.; Egan, R.; Evans, R.; Hogg, D.; Jarnason, S.; Keevers, M.; Lasswell, P.; O’Sullivan, J.; Schubert, U., Turner, A.; Wenham, S.R.; & Young, T (2004) Crystalline silicon on glass (CSG) thin-film solar cell modules Solar energy, Vol 77, pp 857-863 Green, M.A (2007) Thin-film solar cells: review of materials, technologies and commercial status J Materials Science: Materials in Electronics, Vol 18, pp S15-S19 Green, M.A.; Eemery, K.; Hishikawa, Y & Warta, W (2011) Solar cell efficiency tables (version 37) Progress in Photovoltaics, Vol 19, pp 84-92 Gromball, F.; Heemier, J.; Linke, N.; Burchert, M & Müller, J (2004) High rate deposition and in situ doping of silicon films for solar cells on glass Solar Energy Materials and Solar Cells, Vol 84, pp 71-82 Hatano, M.; Moon, S; Lee, M.; Grigoropoulos, C.P & Suzuki, K (2001) Excimer laserinduced melting and resolidification dynamics of silicon thin films J Korean Physical Society, Vol 39, pp S419-S424 Jackson, K.A & Chalmers, B (1956), Kinetics of Solidification Canadian J Physics, Vol 34, pp 473-490 Kunz, T.; Burkert, I.; Gawehns, N & Auer, R (2008) Crystalline silicon thin-film solar cells on graphite or SiC-ceramic substrates Proc 23rd Europ Photovoltaic Solar Energy Conf (2008), pp 2202-2204 Kashchiev, D (1969) Solution of the non-steady state problem in nucleation kinetics Surface Science, Vol 14, pp 209-220 Keevers, M.J.; Young, T.L.; Schubert, U & Green, M.A (2007) 10% efficient CSG minimodules, Proc 22nd Europ Photovoltaic Solar Energy Conference, pp 1783-1790 Kodera, H (1963) Diffusion coefficients of impurities in silicon melt Japanese J Applied Physics, Vol 2, pp 212-219 Kuo, C.-C (2009) Fabrication of large-grain polycrystalline silicon for solar cells Laser Physics, Vol 19, pp 143-147 Lichtenstein, N.; Baettig, R.; Brunner, R.; Müller, J.; Valk, B.; Gawlik, A.; Bergmann, J & Falk, F (2010) Scalable, High Power Line Focus Diode Laser for Crystallizing of Silicon Thin Films Physics Procedia, Vol 5, pp 109-117 Mariucci, L; Pecora, A; Fortunato, G.; Spinella, C & Bongiorno, C (2003) Crystallization mechanisms in laser irradiated thin amorphous silicon films Thin Solid Films, Vol 427, pp 91-95 Michaud, J.F.; Rogel, R.; Mohammed-Brahim, T & Sarret, M (2006) Cw argon ion laser crystallization of silicon films: Structural properties J Non-Crystalline Solids, Vol 352, pp 998-1002 Pihan, E.; Slaoui, A & Maurice, C (2007) Growth kinetics and crystallographic properties of polysilicon thin films formed by aluminium-induced crystallization, J Crystal Growth, Vol 305, pp 88-98 Rau, B.; Sieber, J.; Schneider, J.; Muske, M.; Stöger-Pollach, M.; Schattschneider, P.; Gall, S & Fuhs, W (2004) Low-temperature Si epitaxy on large-grained polycrystalline seed layers by electron-cyclotron resonance chemical vapor deposition J Crystal Growth, Vol 270, pp 396-401 Crystalline Silicon Thin Film Solar Cells 159 Rau, B.; Conrad, E & Gall, S (2006) Influence of post-deposition treatment of absorber layers on poly-Si thin-film solar cells on glass grown by ECRCVD Proc 21st Europ Photovoltaic Solar Energy Conf., pp 1418-1421 Reuter, M.; Brendle, W.; Tobail, O & Werner, J.H (2009) 50 µm thin solar cells with 17.0% efficiency Solar Energy Materials and Solar Cells, Vol 93, pp 704-706 Sarikov, A.; Schneider, J.; Klein, J.; Muske, M & Gall, S (2006) Theoretical study of the initial stage of the aluminium-induced layer-exchange process J Crystal Growth, Vol 287, pp 442-445 Schneider, J.; Sarikov, A.; Klein, J.; Muske, M.; Sieber, J.; Quinn, T.; Reehal, H.S.; Gall, S & Fuhs, W (2006a) A simple model explaining the preferential (100) orientation of silicon thin films made by aluminum-induced layer exchange J Crystal Growth, Vol 287, pp 423-427 Schneider, J.; Schneider, A.; Sarikov, A.; Klein, J.; Muske, M.; Gall, S & Fuhs, W (2006b) Aluminum-induced crystallization: Nucleation and growth process J NonCrystalline Solids, Vol 352, pp 972-97 Schneider, J.; Dore, J.; Christiansen, S.; Falk, F.; Lichtenstein, N.; Valk, B.; Lewandowska, R.; Slaoui, A.; Maeder, X.; Lábár, J.; Sáfrán, G.; Werner, M.; Naumann, V & Hagendorf, C (2010) Solar Cells from Crystalline Silicon on Glass Made by Laser Crystallised Seed Layers and Subsequent Solid Phase Epitaxy Proc 25th Europ Photovoltaic Solar Energy Conf 2010, pp 3573-3676 Sontheimer, T.; Dogan, P.; Becker, C.; Gall, S.; Rech, B.; Schubert, U.; Young, T.; Partlin, S.; Keevers, M & Egan, R.J (2009) 6.7% efficicent poly-Si thin film mini-modules by high-rate electron-beam evaporation Proc 24th Europ Photovoltaic Solar Energy Conf 2009, pp 2478-2481 Straub, A.; Inns, D.; Terry, M.L.; Huang, Y.; Widenborg, P.I & Aberle A.G (2005) Optimisation of low-temperature silicon epitaxy on seeded glass substrates by ionassisted deposition J Crystal Growth, Vol 280, pp 385-400 Teplin, C.W.; Branz, H.M.; Jones, K.M.; Romero, M.J.; Stradins, P & Gall, S (2007) Hot-wire chemical vapor deposition epitaxy on polycrystalline silicon seeds on glass Materials Research Society Symposium Proc., Vol 989-A06-16: Amorphous and Polycrystalline Thin-Film Silicon Science and Technology 2007, pp 133-137 Ujihara, T.; Sazaki, G., Fujiwara, K.; Usami, N & Nakajima, K (2001) Physical model for the evaluation of solid-liquid interfacial tension in silicon J Applied Physics, Vol 90 (2001), pp 750-755 Van Gestel, D.; Gordon, I.; Bender, H.; Saurel, D.; Vanacken, J.; Beaucarne, G & Poortmans, J (2009) Intragrain defects in polycrystalline silicon layers grown by aluminuminduced crystallization and epitaxy for thin-film solar cells J Applied Physics, Vol 105, p 114507 Wang, Z.M ; Wang, J.Y.; Jeurgens, L.P.H & Mittemeijer, E.J (2008) Thermodynamics and mechanism of metal-induced crystallization in immiscible alloy systems: Experiments and calculations on Al/a-Ge and Al/a-Si bilayers Physical Review B, Vol 77, pp 045424 160 Solar Cells – Thin-Film Technologies Werner, J.H.; Dassow, R.; Rinke, T.J.; Köhler, J.R & Bergmann, R.B (2001) From polycrystalline to single crystalline silicon on glass Thin Solid Films, Vol 383, pp 95101 Architectural Design Criteria for Spacecraft Solar Arrays Antonio De Luca VEGA Space GmbH Germany Introduction Scope of this chapter is to provide design criteria for spacecraft solar arrays at system level The design a satellite solar array is usually influenced by several constraints; mission profile, chosen attitude, overall spacecraft configuration, mass and sizing requirements, etc Moreover, its design has to be harmonised with the chosen solar array power conditioning, in order to optimize mass, dimensions, and also particular constraints coming from EMC and thermal environments The chapter is basically composed of the following sections; General description of the current solar cell technologies currently used in space, with particular attention to the triple junction solar cells Mathematical model of an equivalent solar cell circuit, to be used for performance calculations in a numerical simulation environment Mathematical description of a simplified thermal model of a solar array in order to analyse solar array performances in orbit Short definition of cosmic radiation effects The satellite power budget, starting point for the solar array sizing The impact of the power conditioning architecture on the solar array (electrical operative point, EMC considerations) The configuration of the solar array with respect to the spacecraft Some design examples for different missions and satellite configurations Numerical simulations of solar array performances as function of the mission profile (orbit propagation, slew manoeuvres, attitudes of particular interest) Solar cells for space applications Since the beginning of the astronautic era, photovoltaic devices have been considered for the generation of electrical power on board spacecrafts because of their high power output per unit mass, associated with the fundamental advantage of not having moving parts, present, instead, in all the most used electrical power generators for both terrestrial and aeronautical applications (turbines, motors, alternators, etc.) Therefore the PV array is static, does not produce vibrations or noise, and does not need an active cooling The Russians were the first, in 1958, to launch a satellite powered with silicon solar cells 162 Solar Cells – Thin-Film Technologies Solar cells for space applications have to be highly efficient, capable to stand thousands of thermal cycles in orbit where the temperature, according to the mission profile may vary from -150 °C to more than 120 °C They have to show a limited degradation during time due to cosmic radiations and Ultraviolet, and they have to resist to the mechanical solicitations mainly linear accelerations and vibrations during launch and orbital manoeuvres, because of these constraints the cells for space are smaller than those for terrestrial applications In order to have the highest conversion efficiency, solar cells for space application are developed from mono-crystalline materials In the past silicon was the most used and the reachable bulk efficiency was not higher than 14% The advent of GaAs based solar cells in the last decade of the 20th century took the efficiency up to 19%, and nowadays triple junction solar cells show more than 30% Figure shows a very simplified structure of triple junction cell Front metal Tunnel junctions Metal p p p n GaInP n GaAs n Ge Fig Triple junction solar cell structure While figure reports the quantum efficiency for each junction, it can be clearly seen that the increased efficiency is due to wider wavelength coverage of the absorbed radiation Fig Equivalent quantum efficiency as function of wavelength Triple junction GaAs solar cells are populating more and more solar generators worldwide, while manufacturers are actively working on four to six junction cells as a way forward always increasing conversion efficiency Consequently, there is a need to improve the understanding of the electrical dynamic behaviour of multi-junction based solar array considering that the proper design of solar array regulators requires, among others, a good mastering of the solar section/regulator interface In order to better understand EMC aspects connected to the chosen regulation philosophy, which will be discussed further, it is worth to have a quick look at the equivalent capacitance present at the output of a triple junction cell The figure reports the capacitance measured across strings composed of 15 cells The cells used are produced by AZUR SPACE Solar Power GmbH It can be observed that at high voltages the capacitance is considerably increased Such behaviour has to be 163 Architectural Design Criteria for Spacecraft Solar Arrays taken into account when the power conditioning architecture is chosen, and the relevant devices designed Capacitance (nF) Gaget2 3G28 500 450 400 350 300 250 200 150 100 50 0 10 20 30 40 50 String voltage (V) Fig Capacitance identified for the 15 cells string, Gaget2 and 3G28 (AZUR SPACE products) Solar cell equivalent circuit The mathematical model of a photovoltaic cell has to take into account the following factors capable to influence the solar cell behaviour Intensity of the incident light Operative absolute temperature Degradation by cosmic radiation The solar cell model, derived from the Mottet-Sombrin’s one, is basically a current generator driven by the value of the voltage applied at its terminal according to the equivalent circuit reported below Generally speaking a solar cell is a particular p-n junction where the diffusion process (diode D1) co-exists with the generation and recombination effect of the charge carrier (diode D2) induced by the presence of crystalline defects This model was tested using data relevant to the AZUR SPACE 28% solar cell, as reported in the datasheet provided by the Manufacturer, and available on company web-site RS VD iL iD D1 iR D2 RP iO VO RO Fig Equivalent Circuit of solar cell The relevant Kirchhoff equations are:    q  VD    q  VD   VD io  iL  iD   exp    1  iR  exp  k  T   1  R  k T        p (1a) 164 Solar Cells – Thin-Film Technologies Vo  VD  RS  io (1b) Where: K=1.381×10-23 (J/°K) is the Boltzmann constant; q=1.602×10-19 (C) is the electron charge; iL, iD e iR are respectively the current due to illumination, and the reverse currents of the diodes D1 e D2; they are function of the temperature The equations (1) give the output voltage Vo, and current Io as function of the voltage drop Vd over the diodes D1 and D2 The second and third term of (1a) represent the typical voltage-current laws of the diodes, and the currents iD and iR are the reverse currents of the diodes dependent from the physics of the solar cell In general, the solar cell is characterised by the following data provided in the manufacturer’s data sheet, the table below gives the values relevant to the one used for testing the model: Isc 506.0 mA Short circuit current; Imp Vmp 487.0 mA Maximum power current; 2371.0 mV Maximum power voltage; Voc 2667.0 mV Open circuit voltage; dIsc/dT dImp/dT 0.32 mA/°K Short circuit current temperature coefficient 0.28 mA/°K Max power current temperature coefficient dVmp/dT -6.1 mV/°K Max power voltage temperature coefficient; dVoc/dT -6.0 mV/°K Open circuit voltage temperature coefficient Such data are given in AM0 (1367.0 W/m2) conditions at Tref=28 °C (301.15 °K) reference temperature Usually the series resistance is around 300mΩ for a triple junction cell, while for the shunt one 500Ω maybe assumed Such resistances may be considered in a first approximation as constant in the operating temperature range of the cell The values of iL, iD and iR at the reference temperature can be calculated with the (1) in the three main point of the V-I curve; short circuit, maximum power and open circuit, by the least square method The next step is to define how these currents change with temperature Concerning iD e iR it is possible to write:  Eg  iD  C D  T 5/2  exp      n1  T  (2a)  Eg  iR  C R  exp      n2  k  T  (2b) Where CD and CR are constants independent from temperature, and Eg is the Energy of the prohibited band gap: Eg  E g   e T2  T   e  (mA/cm2) (3) 165 Architectural Design Criteria for Spacecraft Solar Arrays With Eg0 = 1.41 eV, αe=-6.6×10-4 eV/°K, and βe=552 °K The current iL due to illumination is given instead by iL T   K T    T   J tot (mA/cm2) (4) Where Jtot is light intensity (W/ m2), η(T) is the efficiency of the cell, K(T) is a coefficient to be determined as function of the temperature n1 e n2 are two coefficients depending on the adopted solar cell technology: At this point all the terms of the equations (1) can be defined at any temperature and by setting as input the operating voltage Vo and solving the system by the Newton-Raphson numerical scheme is possible to calculate the output current io Figure shows the V-I curves relevant to Triple Junction AZUR SPACE solar cell starting from the datasheet available on the web site, as function of temperature at Begin Of Life (BOL); the black asterisks are the maximum power points calculated according to the datasheet In figure V-I curves for different illumination levels are reported AZUR Space 3G 28% BOL, 1367 W/m2 0.7 440 K 400 K 360 K 320 K 280 K 240 K 200 K 160 K 120 K 0.6 0.5 Current [A ] 0.4 0.3 0.2 0.1 0 0.5 1.5 voltage [V] 2.5 3.5 Fig Computed V-I curves as function of temperature using AZUR SPACE 3G 28% data Azur Space 3G 28%, BOL @300K 0.7 0.6 1367 W/m2 0.4 1000 W/m2 C urren t [A ] 0.5 500 W/m2 0.3 250 W/m2 0.2 100 W/m2 0.1 0 0.5 1.5 Voltage [V] 2.5 3.5 Fig Computed V-I curves as function of illumination using AZUR SPACE 3G 28% data 166 Solar Cells – Thin-Film Technologies Solar panel thermal model What said above clearly highlights the need of a thermal model of the solar panel taking into consideration the heat exchange on both sides of it in case of a deployable one; or usually considering the rear side as adiabatic in case of the panel is body mounted The panel is considered as rigid, with honeycomb structure on which the solar cells are applied; the following table reports the components recognizable in solar panel cross-section: Components from front to rear side Coverglass Coverglass adhesive Solar cell Cell adhesive Kapton insulation Face skin (Carbon fibre) Adhesive Honeycomb (Aluminium) Adhesive Face skin (Carbon fibre) Black paint Thickness, μm 150 - 500 50 - 100 100 - 200 100 50 100 Up to cm 100 50 Table Solar panel composition The panel temperature is computed taking into account the direct sun radiation, the albedo radiation, the irradiation to deep space, and irradiation between the earth surface and the panel itself The sun illumination is variable during the year and considering only missions around the earth it may range between 1315.0 (summer solstice) and 1426 W/m2 (winter solstice), while the albedo of the earth surface is about 30% of the incident sun illumination The panel exchanges heat with the deep space and this is seen as a black body at 3°K, as well as the earth irradiates as a black body at 250°K The following simplifying assumptions can been made; a deployed solar panel does not exchange heat with the outer surfaces of the satellite body, a body mounted solar panel is adiabatically isolated from the rest of the satellite body and finally the panel surface temperature is considered as uniform The conduction across the panel also plays an important role, and it has to be taken into account in case of a deployed solar panel At a first glance, the in-plane conductivity may be neglected, this because under the hypothesis of uniform temperature over the panel, the heat exchange between adjacent cells is basically zero The thermal equilibrium is computed by solving the differential equation which takes into account the different heat exchange modalities C dT  QRad  QAlb  QEarth  QSpace  Qcond dt (5) Where: Q Rad       cos   J (6) 167 Architectural Design Criteria for Spacecraft Solar Arrays It is the contribution of the direct sun radiation J that is not converted into electrical power by the photovoltaic cell; Q alb        F  Al  F1   J (7) It is the contribution of the albedo radiation; QEarth      F12  (TE  T ) (8) It is the heat exchanged with the Earth surface QSpace      (1  F12 )  T (9) It is the heat released to the deep space Qcond  Tfront  Trear   k x (10) Is the heat transmitted by conduction between the front and rear faces of the panel at Tfront and Trear temperature respectively The parameters appearing in these equations have the following meanings: C = thermal capacitance of the panel per unit area, main contribution is provided the honeycomb structure;  = solar cell absorptivity;  = solar cell emissivity; Al = albedo coefficient, about 0.3 for earth; F = albedo visibility factor; F12 = View factor between radiating surface and planet  = Stephan-Boltzmann, constant: 5.67210-8 W/(m2°K4); TE = Black body equivalent temperature of the earth;  = incidence angle of the sunlight on the panel; k = panel transverse thermal conductivity; Δx =panel thickness; The radiating view factor of a flat surface with respect to the Earth surface is function of the altitude h, earth radium R  and the angle λ between the nadir and the normal to the panel The albedo view factor is computed according to the following formulas:   Falb  1  cos  app   cos      (11) Where β is the angle between the nadir and the earth-sun direction:  R    h  R   app  arcsin  (12) The integration in the time domain of the equation (5) gives the actual temperature of the panel along the propagation of the orbit in eclipse and sunlight, taking into account the orientation of the panel itself with respect to the earth and the sun The thermal model 168 Solar Cells – Thin-Film Technologies exposed so far is sufficient for the design of a solar array for space application at system level 0.9 0° 0.8 20° 0.7 40° 0.6 50° 0.5 View factor F12 60° 70° 0.4 80° 0.3 90° 0.2 100° 0.1 180° 10 160° 20 110° 120° 130° 140° 30 40 50 60 70 Sat Altitude-Earth radium ratio (H=h/R) 80 90 100 Fig View Factors F12 as function of H=h/R, parameter: 10 Albedo visibility factor as function of altitude, for different values of Beta angle 80 deg 70 deg 60 deg 30 deg deg Altitude [km] 10 10 10 -4 10 -3 10 -2 10 Visibility Factor F -1 10 10 Fig Albedo Visibility factor F as function of h for different β value Degradation due to space environment Space is a hostile environment for the electronic components in general and solar cells in particular The sun radiates energy in almost the whole electromagnetic spectrum, from radio waves to gamma rays, and abundant charged particles impinging on a surface cause damages which cumulate over the mission lifetime (fluence Φ) The behaviour of solar cells in a radiation environment can be described in terms of the changes in the engineering output parameters of the devices The radiation usually of interest in the study of degradation of materials and devices consists of energetic or fast massive particles (i.e electrons, protons, neutrons or ions) The major types of radiation damage phenomena in ... electron beam crystallized thin film silicon 1 56 Solar Cells – Thin- Film Technologies solar cells on glass substrates Proc 24th Europ Photovoltaic Solar Energy Conf., pp 25 06- 2509 Andrä, G.; Bergmann,... discovered as a useful substrate 142 Solar Cells – Thin- Film Technologies for thin film transistor applications (Michaud et al., 20 06) as well as for solar cells (Andrä et al., 1998; Andrä et... efficient thinfilm polycrystalline-silicon solar cells based on aluminum-induced crystallization and thermal CVD Progress in Photovoltaics, Vol 15, pp 575-5 86 158 Solar Cells – Thin- Film Technologies